Happy Valley is the only available camping area in Rural County. It is owned by the county, which allows free access to campers. Almost all visitors to Happy Valley come from the six towns in the county.

Rural County is considering leasing Happy Valley for logging, which would require that it be closed to campers. Before approving the lease, the county executive would like to know the magnitude of annual benefits that campers would forgo if Happy Valley were to be closed to the public.

An analyst for the county has collected data for a travel cost study to estimate the benefits of Happy Valley camping. On five randomly selected days, he recorded the license plates of vehicles parked overnight in the Happy Valley lot. (Because the camping season is 100 days, he assumed that this would constitute a 5 percent sample.) With cooperation from the state motor vehicle department, he was able to find the town of residence of the owner of each vehicle. He also observed a sample of vehicles from which he estimated that each vehicle carried 4 persons (2 adults), on average. The spreadsheet included in the week 5 module summarizes the data he collected.

In order to translate the distance traveled into an estimate of the cost campers faced in using Happy Valley, the analyst made the following assumptions. First, the average operating cost of vehicles is $0.40 per mile. Second, the average speed on county highways is 60 miles per hour. Third, the opportunity cost to adults of travel time is 40% of their wage rate; it is zero for children. Fourth, adult campers have the average county wage rate of $10 per hour.

The analyst has asked you to help him use this information to estimate the annual benefits accruing to Happy Valley campers. Specifically, assist with the following tasks.

First, use the preceding information to calculate the travel cost per trip from each of the six towns. (Use two decimals for your answers below.) The data for is attached.

Question:

What is the TC (travel cost) from town A? B? C? D? E? F?

Next, for the six towns, use Excel to regress visit rate (VR) on travel cost per person (TCp) and a constant. Before running the regression you need to calculate TCp for each town.

What is the slope of the fitted line? (Note that the slope is negative, so include a - in your answer. Also include two decimal points.)

You know that with the current free admission the number of camping visits demanded is 14,160. Find additional points on the demand curve by predicting the reduction in the number of campers from each town as price is increased by $5 increments until demand falls to zero. This is done in three steps at each price: first, use the coefficient of TCp from the regression (your answer for question 7) to predict a new visit rate (VR) for each town. Second, multiply the predicted VR of each town by its population to get a predicted number of visitors. Third, sum the visitors from each town to get the total number of predicted visits. (In your answers for questions 8-12 do not include a comma or a decimal point.)

Total predicted visits to Happy Valley with fee of $5? $10? $15? $20? $25?

What is estimated area under demand curve as the annual benefit to campers?

Town Miles from Happy Valley Population (thousands) Number of vehicles Estimated number of Visit rate (visits per in sample visitors for season 1000 people) 146 3893 2267 50.1 34.9 15.6 89.9 98.3 22 587 77.7 65 37.6 53.4 19.8 11 180 4800 1947 60.4 666 TOTAL 14160 Town Miles from Happy Valley Population (thousands) Number of vehicles Estimated number of Visit rate (visits per in sample visitors for season 1000 people) 146 3893 2267 50.1 34.9 15.6 89.9 98.3 22 587 77.7 65 37.6 53.4 19.8 11 180 4800 1947 60.4 666 TOTAL 14160